If you're arriving in to Boston and heading to anywhere along the Green Line, keep in kind that Government Center station (for transfers between blue and green) is closed. Instead, take the Massport shuttle to Copley or Hynes convention center.

The hotels located on airport property are the Hilton Boston Logan Airport and the Hyatt Harborside.
The Hilton Boston Logan Airport has beautifully appointed guest rooms with a direct connection via an enclosed sky bridge to Boston Logan's terminals as well as round-the-clock, complimentary shuttle service to all airline terminals, subway station and water taxi

The closer you park to your terminal, the more expensive the rate is. Rates start at $18 per day for economy lots. Free shuttle. Regular rate lots closer to the terminals start at $27 per day. Massport maintains a Logan Parking Conditions website; It is wise to use it.